Quasinormal modes of scalar field coupled to Einstein's tensor in the non-commutative geometry inspired black hole

We investigate the quasinormal modes (QNMs) of scalar field coupled to Einstein's tensor in non-commutative geometry inspired black hole spacetime. It is found that lapse function metric can be represented by a Kummer's confluent hypergeometric function, which effectively solve problem numerical results QNMs are sensitive model parameters and make values more reliable. careful analysis QNM frequencies using several methods, find obtained new WKB method (the Pad\'e approximants) Mashhoon (P$\ddot{\text{o}}$schl-Teller potential method) quite different from those asymptotic iterative (AIM) time-domain integration when parameter $\theta$ coupling $\eta$ large. The most obvious difference AIM appear critical value $\eta_c$ with an increase $\eta$, leads dynamical instability. After carefully analyzing numeral results, we conclude closer theoretical than method, Moreover, through fitting, obtain functional relationship between threshold satisfies $\eta_{c}=a\theta^{b}+c$ for fixed $l$ approximately. stability dynamics ensured $\eta<\eta_c(\theta, l)$ region.